2player game connecting with line segments 1,2,...,2020 on blackboard
Source: 2020 Czech-Polish-Slovak Match p3
October 8, 2020
combinatoricsgamegame strategywinning strategy
Problem Statement
The numbers are written on the blackboard. Venus and Serena play the following game. First, Venus connects by a line segment two numbers such that one of them divides the other. Then Serena connects by a line segment two numbers which has not been connected and such that one of them divides the other. Then Venus again and they continue until there is a triangle with one vertex in , i.e. is connected to two numbers that are connected with each other. The girl that has drawn the last line segment (completed the triangle) is the winner. Which of the girls has a winning strategy? (Tomáš Bárta, Czech Republic)